Large deviations of a modified Jackson network: Stability and rough asymptotics

By R. Foley, D. McDonald. 2005

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Consider a modified, stable, two node Jackson network where server 2 helps server 1 when server 2 is idle. The probability of a large deviation of the number of customers at node one can be calculated using the flat boundary theory of Schwartz and Weiss [Large Deviations Performance Analysis (1994), Chapman and Hall, New York]. Surprisingly, however, these calculations show that the proportion of time spent on the boundary, where server 2 is idle, may be zero. This is in sharp contrast to the unmodified Jackson network which spends a nonzero proportion of time on this boundary.

Subfields: Management Information Systems, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/a36d61a3c76461af230fb77f14ff331b53e9d5f8